The lengths of a right triangle's three sides can be expressed as 24, 32, and 40.
Let's work our way through the solution. According to the right triangle formula, a triangle's hypotenuse square equals the sum of its base square and its altitude square.
How to determine a right triangle's sides?
If leg an is absent, change the equation to its form when leg an is present on one side and compute the square root: a = (c2 - b2).
Leg b must be unknown otherwise. b = √(c² - a²)
The equation for hypotenuse c is: c = (a2 + b2)
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Answer with Step-by-step explanation:
a.

Taking both sides log

Using identity:

Using identity:


b.
We know that

Using identity

c.

Substitute the values then we get

By using 
Hence, 
Answer:
A political strategist wants to test the claim that the percentage of residents who favor construction is more than 30%, so then that represent our claim and needs to be on the alternative hypothesis.
Based on this the correct system of hypothesis are:
Null hypothesis: 
Alternative hypothesis 
Step-by-step explanation:
We have the following info given from the problem:
the random sample of voters selected from the town
represent the proportion of residents favored construction
represent the value desired to test.
A political strategist wants to test the claim that the percentage of residents who favor construction is more than 30%, so then that represent our claim and needs to be on the alternative hypothesis.
Based on this the correct system of hypothesis are:
Null hypothesis: 
Alternative hypothesis 
And in order to test this hypothesis we can use a one sample z test for a population proportion and the statistic would be given by:
(1)
And with the data given we have:
Answer is A or your first option.